Finite Group Databasebeta

← #29577628

Subgroups — #29577628

Order 15616.

452 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454921C211yesmaximal, characteristic, complemented
2#21444557C211yesmaximal, characteristic, complemented
3#21444487C212yesmaximal
4#21443709C212yesmaximal, complemented
5C61×#3138C211yesmaximal, characteristic
6#16839893—22no—
7Q8×#92418—22no—
8#16839823—22no—
9#16839815C2212yes—
10#16839786C2212yes—
11#16839508—22no—
12#16839506—22no—
13#16839506—22no—
14C61×#533C2211yescharacteristic
15C2×#127×C61C2211yescharacteristic
16C61×#490C414yes—
17C61×#486—22no—
18C61×#418—22no—
19C4×M16×C61C2211yescharacteristic
20C2×#11758194—22no—
21C4⋊#92418—24no—
22C4⋊#92418—22no—
23C4⋊#92418—22no—
24C4⋊#92418D412yes—
25C4⋊#92418D412yes—
26C22⋊#92418—22no—
27#14519688—22no—
28C4×#92418—22no—
29C4×#92418—22no—
30C22×D4×C61—21no—
31C22×D4×C61—22no—
32C2×M16×C61—21no—
33C4⋊Q8×C61D412yes—
34#127×C61—22no—
35#127×C61—21no—
36#127×C61C2×C412yes—
37#125×C61C2×C412yes—
38C22⋊Q8×C61—22no—
39C4×Q8×C61—22no—
40#117×C61D412yes—
41C2×C42×C61C2311yescharacteristic
42#102×C61—28no—
43#97×C61C2×C412yes—
44C4×C8×C61—21no—
45C24×C61—41no—
46C2×Q8×C61—22no—
47C2×D4×C61—22no—
48C2×D4×C61—24no—
49C2×D4×C61—44no—
50C2×D4×C61—41no—
51C2×D4×C61—42no—
52C2×D4×C61—82no—
53C2×D4×C61—82no—
54C22×C4×C61C2×D411yescharacteristic
55C22×C4×C61#4112yes—
56M16×C61—42no—
57C2×C8×C61—22no—
58C4⋊C4×C61—24no—
59C4⋊C4×C61—22no—
60C4⋊C4×C61C22⋊C414yes—
61C22⋊C4×C61—22no—
62C42×C61—22no—
63C42×C61C22×C411yescharacteristic
64C42×C61C2×D411yescharacteristic
65C42×C61C2×D412yes—
66#11758194—82no—
67C2×#92418—22no—
68C2×#92418—22no—
69C2×#92418—42no—
70C23×C61—42no—
71C23×C61—82no—
72C23×C61—84no—
73C23×C61#12311yescharacteristic
74Q8×C61—42no—
75Q8×C61—42no—
76D4×C61—44no—
77D4×C61—84no—
78D4×C61—82no—
79D4×C61—82no—
80D4×C61—82no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—24no—
85C2×C4×C61C2×C22⋊C411yescharacteristic
86C2×C4×C61C4×D412yes—
87C2×C4×C61#12011yescharacteristic
88C2×C4×C61#12112yes—
89C8×C61—42no—
90#92418—42no—
91#92418—42no—
92#92418—82no—
93#9438—611nomaximal, Sylow
94C22×C61—21no—
95C22×C61—22no—
96C22×C61—82no—
97C22×C61—84no—
98C22×C61—164no—
99C22×C61#38611yescharacteristic
100C4×C61—21no—
101C4×C61—22no—
102C4×C61—44no—
103C4×C61#45412yes—
104C4×C61#47112yes—
105C4×C61#47212yes—
106#3138D6111yescharacteristic
107#2986—611no—
108#1561—611no—
109#1545—612no—
110#1299—612no—
111C2×C61—41no—
112C2×C61—162no—
113C2×C61#188811yescharacteristic
114C2×C61#190712yes—
115#533C2×D6111yescharacteristic
116C2×#127C2×D6111yescharacteristic
117#490Dic6114yes—
118#486—22no—
119#446—1222no—
120C8×Q8—1222no—
121#433—1222no—
122#431—612no—
123#423—612no—
124#418—22no—
125C4×M16C2×D6111yescharacteristic
126#332—1222no—
127#331—1222no—
128#331—1222no—
129C61#943811yescharacteristic, complemented, Sylow
130C22×D4—22no—
131C22×D4—21no—
132C2×M16—21no—
133C2×M16—1222no—
134C4⋊Q8C22⋊D6112yes—
135#127—22no—
136#127—21no—
137#127C2×Dic6112yes—
138#125C2×Dic6112yes—
139C22⋊Q8—22no—
140C4×Q8—22no—
141#117C22⋊D6112yes—
142C2×C42C22×D6111yescharacteristic
143C4⋊C8—612no—
144C4⋊C8—612no—
145C4⋊C8—1224no—
146C4⋊C8—1222no—
147C4⋊C8—1222no—
148#102—28no—
149C22⋊C8—1222no—
150#97—1222no—
151#97C2×Dic6112yes—
152C4×C8—21no—
153C4×C8—1222no—
154C4×C8—1222no—
155C24—41no—
156C2×Q8—22no—
157C2×D4—22no—
158C2×D4—24no—
159C2×D4—44no—
160C2×D4—41no—
161C2×D4—42no—
162C2×D4—82no—
163C2×D4—82no—
164C22×C4#1175822412yes—
165C22×C4C2×C22⋊D6111yescharacteristic
166M16—42no—
167M16—4882no—
168C2×C8—22no—
169C2×C8—1222no—
170C2×C8—1222no—
171C2×C8—2442no—
172C4⋊C4—24no—
173C4⋊C4—22no—
174C4⋊C4C22⋊Dic6114yes—
175C22⋊C4—22no—
176C42—22no—
177C42D4×D6112yes—
178C42C22×Dic6111yescharacteristic
179C42C2×C22⋊D6111yescharacteristic
180C23—42no—
181C23—82no—
182C23—84no—
183C23#1451975811yescharacteristic
184Q8—42no—
185Q8—42no—
186D4—44no—
187D4—84no—
188D4—82no—
189D4—82no—
190D4—82no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4C2×C22⋊Dic6111yescharacteristic
196C2×C4D4×Dic6112yes—
197C2×C4#1451974511yescharacteristic
198C2×C4#1451974912yes—
199C8—42no—
200C8—4882no—
201C8—2442no—
202C8—2442no—
203C22—21no—
204C22—22no—
205C22—82no—
206C22—84no—
207C22—164no—
208C22#1683964211yescharacteristic
209C4—21no—
210C4—22no—
211C4—44no—
212C4#1683993412yes—
213C4#1684002312yes—
214C4#1684003012yes—
215C2—41no—
216C2—162no—
217C2#2144622311yescharacteristic
218C2#2144632912yes—
subgroupG/H
centerC22#16839642
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#3138C2
socleC22×C61#386
prime radicalC2×#127×C61C22
cosocleC2×C42×C61C23
hypercenter#3138D61
hypocenterC61#9438
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3138

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #21454921C2semidirect
2. #21444557C2semidirect
4. #21443709C2semidirect
129. C61#9438semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214549212
#214445572
#214444872
#214437092
C61×#31382
#943861